Imagine a clock that will keep perfect time forever, even after the heat-death of the universe. This is the “wow” factor behind a device known as a “space-time crystal,” a four-dimensional crystal that has periodic structure in time as well as space.

Bold prediction.

Let me say at the outset that I don’t implicitly trust any press release, especially one that gets quantum entanglement wrong or explains it way too vaguely (“an action on one particle impacts another particle” No!), as this one does, so it’s possible this wasn’t fully vetted by the scientists involved.

But there are other reasons to think they are overselling the experiment here. Let me say at the outset that I find the proposal intriguing; it’s not the physics that is in question, and the claims in the press release are not present in the paper. It’s those promises, of what we’ll be able to do with the experiment, that give me pause. Namely:

Imagine a clock that will keep perfect time forever, even after the heat-death of the universe.

Ok, yeah, about that. It might be fair to claim an atom, or possibly a molecule, will survive the heat death of the universe, but a macroscopic device? The device forms a quantum-mechanical oscillator with an ion trap, requiring a certain configuration of electric and magnetic fields, i.e. this space-time crystal is not a physical crystal. Somehow I doubt that the equipment running it will last forever.

If we lose the expectation that this will last a super long time, we still have the idea that it will be a perfect clock, right? Why is this supposed to be perfect?

The persistent rotation of trapped ions produces temporal order, leading to the formation of a space-time crystal at the lowest quantum energy state.

Because the space-time crystal is already at its lowest quantum energy state, its temporal order – or timekeeping – will theoretically persist [for a long time]

It’s true that a quantum mechanical ground state can persist without violating any laws of thermodynamics, and the ground state of a system has a frequency that is infinitely narrow — excited states have a width that is dictated by the uncertainty relation $latex \Delta{E}\Delta{t}>\hbar/2 $ but a ground state has an infinite lifetime. Thus, no time uncertainty.

However… (you knew this was coming)

The paper shows that the rotation frequency of the ions in the crystal depends on the magnetic field you apply to it. That magnetic field will not have a perfectly precise value — it will have fluctuations in it, which means that the oscillation frequency is not going to be a delta function — there will be uncertainty.

Not only that, but how do you count the oscillations and discern the phase? That introduces error into any clock — the perturbation of measurement. In most atomic clocks you have a transition at some frequency, and the excited state does have some width to it, which is why long-lived transitions are used whenever possible — it means the transition will be narrow — but the proposal for this clock is to measure where a particular ion is by shining a spatially narrow laser on it. So they aren’t leveraging the infinitely narrow state; I don’t think they can. The mental picture I have is that it would be like counting a wheel’s rotation by painting a spot on its rim and counting how many rotations you have. The problem is that any ion is going to have an inherent location uncertainty, and the laser will add to that because the spot will likewise have a spatial extent. So even if that’s small, it won’t vanish — there will be a measurement uncertainty introduced, on top of the frequency uncertainty from the magnetic field. Not perfect.

Go ahead and blame me for being the reason we can’t have nice things that are perfect and last beyond the heat death of the universe.